I changed the symbols in the formula to this:
This I can remember with the phrase 'a touchdown equals the quarterback plus the receiver'.
T = Top of the fraction
Q = Quotient
B = Bottom of the fraction
R = Remainder
A numerical example is this:
13 Ã· 4 = 3 R 1
However, you should remember that it really is just 13 Ã· 4 = 3 + 1/4 or 3.25. So you see that the ".25" part of the answer is just "R / B". If we can write the decimal part as a fraction, then we can determine what might be the remainder.
In your example:
If T divided by B equals 8.12 what is a possible remainder?
We just need to figure out how express ".12" into a fraction. Well, the easy fraction here is "12/100." This can be simplified to "3 / 25" which is "R / B". So we know that the remainder must be a multiple of 3 for this to be true.
Hope that makes sense.